I've used mosh on and off for the past year. For me, the best feature of mosh is the support for roaming. For the "persistence" aspect, SSH + remote screen is sufficient.

There was a point where I used mosh whether I was roaming or sitting at my desk, but eventually the friction of mosh made it only worthwhile to use in roaming situations. By "friction" I mean the small annoyances of (1) installing mosh on every new server, and (2) requiring the use of screen to get scrollback buffers. I frequently use screen in my workflows outside of mosh, so I would often end up in weird states where I moshed into a server and auto-attached to my dedicated "moshscreen," but then had to detach from it within the session to move to another screen that I wanted to use.

Because of those annoyances, I now just use simple SSH when sitting at my desk, and put any long-running commands into a remote screen. But mosh is still extremely useful in two narrow cases: train rides (moving between cell towers) and traveling in developing countries (high packet loss).